Question 59923
It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together?
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Cindy DATA:
Time = x hrs./job  ; Rate = 1/x job/hr.
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Eva DATA:
Time = x+3 hrs/job  ; Rate = 1/(x+3) job/hr.
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Together DATA:
Rate = 1/x + 1/(x+3) = (2x+3)/(x^2+3x) job/hr

EQUATION:
Cindy worked 8 hrs.
Eva worked 6 hours.
8*(cindy rate) + 6(eva rate)= 0.9 job
8/x + 6/(x+3) = 9/10
8(x+3)10 + 6x(10)=9x(x+3)
80x+240+60x = 9x^2+27x
9x^2-113x-240=0
x=[113+-sqrt(113^2-4*9*-240]/18
x=[113+-sqrt21409]/18
x=[113+146,3181]/18
x=14.41 hrs
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If x = 14.41 the "working together rate" is 
(2x+3)/(x^2+3x) job/hr = (31.81)/(14.41^2+3(14.41))=31.81/250.88 job/hr
EQUATION:
Let z be the number of hours required to "finish the job" 
(finish the job means do 0.1 of it).
So, (31.81/250.88) z = 0.1
z=0.788 hr
z=0.788(60)=47.32 minutes (time required for them to finish the job together)
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Cheers,
Stan H.